Trigonometry Examples

$x^{2} = 11 x - 10$

Step 1

Subtract $11 x$ from both sides of the equation.

$x^{2} - 11 x = - 10$

Step 2

Add $10$ to both sides of the equation.

$x^{2} - 11 x + 10 = 0$

Step 3

Factor $x^{2} - 11 x + 10$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $10$ and whose sum is $- 11$ .

$- 10, - 1$

Step 3.2

Write the factored form using these integers.

$(x - 10) (x - 1) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 10 = 0$

$x - 1 = 0$

Step 5

Set $x - 10$ equal to $0$ and solve for $x$ .

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Step 5.1

Set $x - 10$ equal to $0$ .

$x - 10 = 0$

Step 5.2

Add $10$ to both sides of the equation.

$x = 10$

Step 6

Set $x - 1$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - 1$ equal to $0$ .

$x - 1 = 0$

Step 6.2

Add $1$ to both sides of the equation.

$x = 1$

Step 7

The final solution is all the values that make $(x - 10) (x - 1) = 0$ true.

$x = 10, 1$